a philosophical perspective on alhazen's optics

Arabic Sciences and Philosophy, vol. 15 (2005) pp. 189–218doi:10.1017/S0957423905000172 � 2005 Cambridge University Press

A PHILOSOPHICAL PERSPECTIVE ON ALHAZEN’S

OPTICS*

NADER EL-BIZRI

I

Although numerous studies have been conducted on the Optics(Kitab al-Manaz*ir)1 of Alhazen (al-H* asan ibn al-Haytham,d. 1040 C.E.), and on its reception, assimilation and maturationwithin the course of development of the perspectivae traditionsin the history of science and art,2 ambiguities do hitherto stillsurround the epistemological and ontological entailments ofhis theory of visual perception. In addressing this question, our

*This paper complements research e#orts that I have conducted elsewhere; see:Nader El-Bizri, ‘La perception de la profondeur: Alhazen, Berkeley et Merleau-Ponty’, Oriens-Occidens, 5 (2004): 171–84; Nader El-Bizri, ‘La phénoménologie etl’optique géométrique’, Actes du congrès de la Société Internationale d’Histoire desSciences et des Philosophies Arabes et Islamiques (Namur, forthcoming); NaderEl-Bizri, ‘La conception du lieu dans la théorie de la perception d’Alhazen’,invited talk at the CNRS, Paris, 30th April 2004; Nader El-Bizri, ‘Alhazen’soptical and geometrical conception of place’, invited talk at the Institute ofArchitecture, University of Nottingham, 10th March 2004; Nader El-Bizri‘Alhazen’s treatise on place’, Canadian Society for the History and Philosophy ofScience, International Conference, Université Laval, Quebec, 24th May 2001.

1 Ibn al-Haytham (Alhazen), The Optics of Ibn al-Haytham, Books I–III, OnDirect Vision, trans. Abdelhamid I. Sabra, 2 vols. (London, 1989); Ibn al-Haytham,Kitab al-Manaz*ir, ed. Abdelhamid I. Sabra, Books I–III (Kuwait, 1983) and BooksIV–V (Kuwait, 2002). See also: Opticae thesaurus Alhazeni, ed. Friedrich Risner(Basel, 1572; repr. New York, 1972), and the Latin critical edition of De aspectibuswith English translation in: Albert Mark Smith, Alhacen’s Theory of VisualPerception (Philadelphia, 2001). We shall hereafter refer to Alhazen’s Optics asKitab al-Manaz*ir in the body of the text, followed by the book, chapter, andsection numbers, which correspond to Sabra’s Arabic critical edition andannotated English translation.

2 See: David C. Lindberg, ‘Lines of influence in the 13th cent. Optics: Bacon,Witelo, and Pecham’, Speculum, 46 (1971): 66–83; David C. Lindberg, ‘La récep-tion occidentale de l’optique arabe’, in Roshdi Rashed and Régis Morelon (eds.),Histoire des sciences arabes, 3 vols. (Paris, 1997), vol. II: Mathématiques etphysique, pp. 355–68; Martin Kemp, The Science of Art: Optical Themes in WesternArt from Brunelleschi to Seurat (New Haven, 1990); Martin Kemp, GeometricalPerspective from Brunelleschi to Desargues (Oxford, 1984); Martin Kemp, ‘Science,non-science, and nonsense: Brunelleschi’s perspective’, Art History 1, n. 2 (1978):134–61.

inquiry herein is principally philosophical in scope and ourtextual reading combines exegesis with hermeneutics. Whilewe observe the delicate procedures of historiography andphilology, we do not unguardedly assume that they areexhaustive of all rigorous methods of thoughtful investigation.Moreover, in heeding the internal coherence of Alhazen’s text,we do not simply lock his views within reductive contextualchronologies, or readily confine them to epochal matters oftextual transmission. Our endeavour is therefore not exclusivelyset in view of serving the purposes of archival documentation,3even if we preserve a thorough and sound sense of historicity.We ultimately recognize the philosophical pertinence of numer-ous subtle leitmotifs within Alhazen’s thinking that speak to usin an e#ective timely manner, which is significantly relevant inits attuned bearings to the thrust of phenomenological theoriesof perception.4

II

Alhazen advanced in his Kitab al-Manaz*ir a careful distinctionbetween an immediate mode of perception by way of glancing,as idrak bi-al-badıha (comprehensio superficialis or com-prehensio per aspectum), and a contemplative perception, asidrak bi-al-ta’ammul (comprehensio per intuitionem – Kitabal-Manaz*ir, II.4 [5, 20, 33]), which is marked by temporality(laysa yakun illa fı al-zaman). He also noted additional modesof perception, which he referred to as idrak bi-al-istidlal(comprehensio per rationem) and idrak bi-al-tafaqqud (percep-tion by way of scrutiny), while moreover highlighting thatal-idrak bi-al-ta’ammul is in some instances accompanied by

3 This documentary domain is well served by mediaevalists and their bio-bibliographical instruments even though it gets occasionally encumbered by someof their archiving quarrels. Nevertheless, one ought to add that it is hardly a traitof intellectual reasonableness to occasionally arrest thinking in the name ofsustaining the strictures of disciplinary methods, especially when these dofundamentally aim at establishing records, which in general handle texts as ifthey were objectively present relics handed down from the past, rather thanessentially furthering in their reading the unfolding of original thought.

4 A. I. Sabra reminds us in his ‘Preface’ (The Optics, p. xi) that: Alhazen’sOptics ‘belongs as much to the history of Latin medieval and early modernscience as it does to the history of science in medieval Islam’. Moreover, giventhat its reception reached J. Kepler, R. Descartes and C. Huygens, one isprompted to also investigate the prolongations of its philosophical imports,particularly from the standpoint of phenomenological research, which mediatesits inquiries via thematic engagements with the history of philosophy and science.

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prior knowledge (ma‘a taqaddum al-ma‘rifa; cum scientia prae-cedente – Kitab al-Manaz*ir, II.4 [6, 18–19, 33–34]), and as beingat times e#ected by sight (al-bas*ar), and at others by discern-ment (al-tamyız). In distinguishing between the workings ofthese modes of visual perception, Alhazen indicated that par-ticular manifest properties of a given visible object appearwhen sight glances at it, while other subtler properties areperceived by way of contemplation and scrutiny, which in theirturn allow sight to ascertain the true form of the visible object(Kitab al-Manaz*ir, II.4 [1–10]).5

In reflecting on the manner of perceiving particular visibleproperties (al-ma‘anı al-mubs*ara; intentiones visibiles – Kitabal-Manaz*ir, II.3 [43–48]),6 Alhazen made a distinction betweenmujarrad al-h*iss (pure sensation), al-ma‘rifa (recognition), andal-tamyız wa-al-qiyas (discernment and comparative measure /inference).7 While mujarrad al-h*iss perceives light qua lightand colour qua colour, al-ma‘rifa perceives properties in theform of a visible object that have been previously seen orremembered, or the like, and involves some kind of inference(qiyas) in inspecting the signs (al-amarat) of that form (Kitabal-Manaz*ir, II.3 [50–52], II.4 [22]). As for al-tamyız wa-al-qiyas,which is not performed by the sense of sight (Kitab al-Manaz*ir,II.3 [17]), but rather by al-quwwa al-mumayyiza (virtus distinc-tiva; �� ; faculty of discernment) through the

5 Regarding reflections on Alhazen’s theory of visual perception, I refer thereader to: Abdelhamid I. Sabra, ‘Sensation and inference in Alhazen’s theory ofvisual perception’, in Peter K. Machamer and Robert G. Turnbull (eds.), Studiesin Perception: Interrelations in the History of Philosophy and Science (Columbus,1978), pp. 160–85; Abdelhamid I. Sabra, ‘Form in Ibn al-Haytham’s theory ofvision’, Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften, vol. 5(1989): 115–40; Mustafa Nazif, al-H* asan Ibn al-Haytham, buh*uthuhu wa-kushufuhual-bas*ariyya, 2 vols. (Cairo, 1942–3), vol. I; Rashed, ‘L’optique géométrique’, inHistoire des sciences arabes, vol. II; Roshdi Rashed, ‘Optique géométrique etdoctrine optique chez Ibn al-Haytham’, in Optique et mathématiques: Recherchessur l’histoire de la pensée scientifique en arabe (Aldershot, 1992), chapter II, and inArchive for History of Exact Sciences, vol. 6 (1970): 271–98; Graziella FedericiVescovini, Studi sulla prospettiva medievale (Turin, 1965).

6 While Alhazen enumerated twenty-two divisions of particular visibleproperties (Kitab al-Manaz*ir, II.3, [44]), Ptolemy restricted their number to seven.See: Abdelhamid I. Sabra, ‘Ibn al-Haytham’s criticisms of Ptolemy’s Optics’,Journal of the History of Philosophy, 4 (1966): 145–9, p. 146; Albert Lejeune,Euclide et Ptolémée, deux stades de l’optique géométrique grecque (Leuven, 1948),p. 12.

7 It is worthy noting that Alhazen examined the errors of vision (aghlat*al-bas*ar) in reference to mujarrad al-h*iss, al-ma‘rifa, and al-qiyas, respectively inchapters 5, 6 and 7 of Book III of Kitab al-Manaz*ir.

ON ALHAZEN’S OPTICS 191

mediation of the sense of sight, it perceives all the properties,including those perceptible by mujarrad al-h*iss and al-ma‘rifa(Kitab al-Manaz*ir, II.3 [1–25]). Moreover, the perception ofparticular visible properties is aided by imagination (al-takhayyul; imaginatio) and memory (al-dhikr or al-tadhakkur;rememoratio), without being exercised with deliberate orexcessive e#orts (Kitab al-Manaz*ir, II.4 [12–15, 22]).8

Although Alhazen noted that pure sensation perceived lightqua light, and colour qua colour, he did nonetheless argue thatsensation was ultimately e#ected by the last sentient (al-h*assal-akhır; sentiens ultimum) and not by the eye alone (Kitabal-Manaz*ir, I.6 [74]), while basing his conclusion on ananatomical (al-tashrıh* ) examination of the structure of the eye(fı h*ay’at al-bas*ar; Kitab al-Manaz*ir, I.5 [1–39]) and mediat-ing it through an investigation of binocular vision (Kitabal-Manaz*ir, I.6 [69–82]).9 The image formed on the crystalline(al-jalıdiyya) passes through the vitreous (al-zujajiyya) to thehollow optic nerve (al-‘as*aba al-jawfa’), which connects to thecommon nerve (al-‘as*aba al-mushtaraka) as a sensation leadingto the last sentient in the anterior part of the brain (muqaddamal-dimagh). Moreover, and in reference to binocular vision,the beholder, under normal circumstances of sight, perceivesa single visible object with two sound eyes (ma‘a salamatal-bas*arayn). The form of that single visible object occurs onthe surface of the crystalline of each of the eyes. Looking atthat object, two of its forms are received, one in each ofthe eyes. Consequently, two forms, each occurring on thecrystalline, pass via the vitreous to the hollow nerves, and(as sensations) get ultimately unified in the common nerve;thus reaching the last sentient as an ordered single formof a sensible object (al-s*ura al-muttah*ida li-al-mubs*ar al-wah*id).

8 Although Alhazen’s theory of visual perception points to the workings of theratiocinative faculty, this does not readily entail that perception is simply anintentional act of consciousness.

9 See: s*urat al-‘aynayn, a diagram in the Istanbul MS Fatih* 3212, fol. 81b(copied by Ah*mad b. Muh*ammad b. Ja‘far al-‘Askarı; al-Bas*ra, ca. 1083–1084C.E.), reproduced by A. I. Sabra, Plate 1, vol. II, The Optics. For an insight intoAlhazen’s approach to binocular vision, see also: Dominique Raynaud, ‘Ibnal-Haytham sur la vision binoculaire, un précurseur de l’optique physiologique’,Arabic Sciences and Philosophy, 13 (2003): 79–99.

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III

In scrutinizing the features of a given visible object, each of theeyes moves in such a way as to face by its middle that object,rather than look at it peripherally. The visualized structure ofan object of vision, which is made up of all its visible proper-ties, is ascertained, and takes shape in the imagination, by wayof repetition, clarification, discernment and comparative infer-ential measure, as well as being remembered in e#ectingrecognition. Moreover, when sight perceives individuals of thesame species repeatedly and continually, a universal form(s*ura kulliyya; forma universalis) of that species takes shape inthe imagination (mutashakkala fı al-takhayyul; figuratus inimaginationem) and gets recollected in recognition (Kitabal-Manaz*ir, II.4 [8–12, 15–17]). It is by way of imagination thatthe eidetic essence (�’y�� ) of a thing, which is represented by itss*ura al-kulliyya, becomes accessible, and designates the whole-ness of the appearing structural properties of that individualentity and its classing among analogous species. The s*uraal-kulliyya does consequently point to the grasping of thequiddity (ma’iyya or mahiyya) of a corresponding object (Kitabal-Manaz*ir, II.4 [17, 22]), whereby vision points to its eideticessence based on the concreteness of the visual aspects of itsperceived presence, without resorting to induction (al-istiqra’).After all, sight will not perceive the quiddity of an object ithas not seen before, unless it inspects its properties (Kitabal-Manaz*ir, II.4 [22]).

The perception of the plenitude of the form of an object(idrak tashakkul jumlat al-s*ura), which is mediated bythe perception of the apparent traits of that thing (idrakbi-al-amarat; comprehensio per signum), requires an act ofimagination that supplements what is shown of the features ofthat thing with imagined aspects that are hidden from sight.The discerning eye parcels out and measures the visual realityof a spectacle that is experientially continuous. In all of this,the object of vision is seen by way of the reception in the eye ofthe light that propagates linearly in the shape of a virtualvisual cone (makhrut*), with its vertex at the centre of the eyeand its base on the surfaces of the visible object; insofar thatthe distinction is drawn here between the conditions ofsight and those of the rectilinear propagation of light (Kitabal-Manaz*ir, I.2, I.3). The light rays that are structured within


this mathematical model, travel from every point on the litand appearing surfaces of the object, like a punctiform /corpuscular configuration of pointillism. This phenomenonsecures the ordering of the visible aspects of the seen object,while meeting the crystalline humour (al-rut*uba al-jalıdiyya)perpendicularly. As for peripheral visible objects that falloutside the virtual cone of vision, they may be sensed laterallyin terms of refractions on the crystalline.10 Furthermore, visionthrough the middle of the eye, via the axis of the virtual coneof vision, is clearer and more distinct than that which is closerto the extremities or peripheries; and so is the case with thelines surrounding that axis (Kitab al-Manaz*ir, II.2 [30]). In allof this, the form of an object of vision acts in its unifiedplenitude as a geometrical structuring configuration for thegathering of the object’s proper visible aspects in spatial-temporal displacement; that is, either the observer movesaround the object in inspecting it, and / or the object is rotated.While being itself invisible in its fullness, and is directly seenin its wholeness from nowhere, the form of the object of visionin its plenitude does nonetheless ground, in its apparentpermanence and constancy, all the object’s varying visibleaspects that appear in succession, as well as structures theordering of their perceptual manifestation.

A thing in its fullness is never given in immediate vision, it israther revealed in its plenitude by way of perceptual continualsuccessions in the apparition of its aspects. In the continuum ofthe manifold of its appearances a thing is constituted out of itsvisible properties that get revealed in temporal and spatialdisplacement, whereby its shown aspects are grasped as beingthose of a specific unified-thing. The givenness of objects ofvision, in their self-showing, or in the very appearing of theiraspects, remains to be the mode of presentation (praesentatio)of an externality (wujud bi-al-kharij), even though it pointsto a seeming constitutive re-presentation (repraesentatio) inreference to recollection and imagination.11 After all, the

10 The conditions for seeing objects that fall outside the cone of vision, yet thatare sensed in lateral sight by way of refraction, are discussed in: Abdelhamid I.Sabra, ‘Ibn al-Haytham’s revolutionary project in optics: The achievement andthe obstacle’, in Jan P. Hogendijk and Abdelhamid I. Sabra (eds.), The Enterpriseof Science in Islam: New Perspectives (Cambridge, Mass., 2003), pp. 85–119.

11 Deviating from the Latin perceptio (or percipere), the German Wahrnehmung,with its embedded reference to Wahrheit, renders perception in Kantian terms as arepresentation that is accompanied by consciousness. Regarding the implications of

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discerning faculty perceives that what is produced in the eyecomes from outside, and that its agent is external to the eye andnot in contact with it. For, the visual perception of a visibleobject simply ceases upon the eyelids (al-ajfan) being closed orwhen the eye turns away from that object, and it occurs againupon opening the eyelids and turning the eye towards thatobject (Kitab al-Manaz*ir, II.3 [73]).

The presence of visible objects in immediate visual percep-tion points to an act of formal approximation that calls forverification. The true form of a thing (al-s*ura al-h*aqıqiyya;forma vera) is thus subjected to tah*qıq (certificatio or certitudo)that yields a verified ascertained form (s*ura muh*aqqaqa wa-mutayaqqana; forma certificata) in vision, which is more firmlyretained in the soul and in the imagination than the one whichhas not been ascertained (Kitab al-Manaz*ir, II.4 [3–5, 14, 22]).Nonetheless, the workings of recollection, as aided by imagi-nation, do not sustain al-s*ura al-h*aqıqiyya of a thing, given thatall things are subject to change against the horizon of tempor-ality that does not preserve the ascertained veracity of priorknowledge (Kitab al-Manaz*ir, II.4 [29–32]). After all, sight doesnot grasp its object of vision in an ascertained manner, unlessall the object’s visible properties are contemplatively verified,and its aspects are inspected, scrutinised and discernedexperientially, and at the time of perceiving it, whether or notthe observer had a prior knowledge of it under the bestconditions of seeing (Kitab al-Manaz*ir, II.4 [35]).12

IV

The manifestation of a thing in its plenitude through its visibleaspects, which are detected in a continuum of manifold appear-ances, occurs by way of contemplation and spatial-temporaldisplacement. Vision manifests the plenitude of a thing as aconstituted unified structure through the partial givenness ofits apparent aspects in successions of continuous perceptions.This state of a#airs is illustrated by way of perspective,whereby a thing is never seen in its entirety, since, the veryappearing of some of its sides entails that its remaining aspects

this etymology, see: Jean-Pierre Cléro, Théorie de la perception, de l’espace àl’émotion (Paris, 2000), pp. 16–17.

12 We are principally dealing here with the conditions of veridical perception;see also: Sabra, ‘Sensation and inference’, p. 182, n. 27.


are unseen. Hence, a partial un-concealment of an opaqueobject in vision is always associated with the concealmentof some of its surfaces. In visual perception, a visible object,which is given through direct vision and immediate intuition,reveals certain of its surfaces or sides while the remainder of itsaspects are veiled. For instance, when an opaque box that hasthe form of a cube is within my field of vision, I only can seethree of its sides simultaneously, which appear as skewedplanes rather than squares. Nonetheless, when I look at theseintersecting planes, I see a cube with sides as squares. Unlikeits appearing aspects, the orthogonal structure of the cube,which is delimited by square sides, is preserved in its geo-metric form as a solid within the distorting visual e#ects ofperspective. To see the side of a cube as a square in perspective,rather than a slanted plane, I have to look at it frontally(bi-al-muqabala) in such a way that its appearing side faces mein what descriptive geometry refers to as a ‘‘normal view’’.However, from that frontal viewpoint, and from the manner bywhich the visible cube is situated in space in reference to theposition of my eyes, only the side that faces me is seen, whilethe other five surfaces of the cube remain concealed. Havingonly perceived one surface of the cube (namely what refers toits extension in height and width, or in length and breadth),the observer cannot simply ascertain its geometric form as asolid from this frontal viewpoint, unless that cube is ultimatelyseen in inclination, which reveals at least one of its othersurfaces in depth. Either perception is frontal, and the cubefaces the eye in such a way that one of its sides is perpendicularto the axis of the virtual cone of vision (sahm makhrut*al-shu‘a‘ ), and hence appears as a square; or, the third dimen-sion of the cube is shown via an inclination in depth whenviewed laterally (imtidad al-jism fı al-ab‘ad al-thalatha; as perthe perception of solidity – Kitab al-Manaz*ir, II.3 [121–122]).13

Although only three surface planes of an opaque solid cubemay appear concurrently, I still see through them the cube asa structural whole. When looking at a cube in perspective, andseeing only three intersecting skewed surface planes, theapparent deformity of its mathematical sides, which are

13 The radial axis of the virtual cone of vision is itself perpendicular to thesurface of the crystalline; should it become inclined, the forms that occur on thesurface of the crystalline would have a di#erent order and altered structure(Kitab al-Manaz*ir, II.2 [19]).

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squares, is not accidental in visual perception. It is rather thecase that such seeming optical misshapenness, which varieswith the spatial location of the cube, its height, orientation andinclination, as well as its distance from the eye of the observerand the angle under which it is seen, highlights its perceptualreality, which in experience has the apparent semblance ofbeing unlike its imagined geometric structure.

The metric and mathematical formation of the cube as ageometric solid is not what is given in direct vision; rather, thecube in question appears through its aspects as seeminglyslanted intersecting surfaces. Nonetheless, the lived and experi-enced reality points through the apparent distortion of theobject of vision to the mathematical veracity of its unifiedform.14 Instead of simply talking about an unbridgeable dividebetween the object of experience and that of mathematics, bothfind a potential fusion in perception, even though by way ofapproximation (namely, the way a physical body approximatesa geometrical solid). Hence, appearances a$rm the structuralgeometric reality of what is seen. Moreover, this visual state ofa#airs is also confirmed in stereographic projections of axono-metric or isometric views, as well as in pictorial representationsthat are constructed through a geometric linear perspective.However, it is by way of gathered aspects in a continuum ofmanifold appearances that the fullness of the cube gets consti-tuted and its form approximated. And yet, it is via spatial-temporal displacement in scrutinizing these aspects that thewholeness of its structure is verified in its appearances (eitherby the movement of the observer around the object in question,and / or by way of rotating that object).

Seeing the façade of a building leads me to believe that it isthe front of an architectural built form that has spatial depthas well as encloses a concealed interior. Even though I only seeone of its elevations, I assume with perceptual trust that itenfolds spatial configurations. However, it might well be thecase that this perceived façade is only the frontage of anarchitectural installation and is not the elevation of a buildingas I initially perceived it to be. While looking at the façade, I

14 See: Pierre Kaufmann, L’expérience émotionelle de l’espace (Paris, 1967), p. 319;Maurice Merleau-Ponty, Le primat de la perception et ses conséquences philoso-phiques (Paris, 1996), p. 48; Cléro, Théorie de la perception, pp. 41–4. It is similarfactors in pictorial representation that generated the experimental forms of Cubism.


assumed, as well as imagined, that I was looking at a build-ing with an internal depth. However, after moving aroundthis structure, and even attempting to access its presumedinterior through its frontal elevation, I realize that what I haveassumed and imagined earlier as being a building is in realitynone other than a mock installation. What I saw as being abuilding through its appearing aspects turned out to beanother type of built-structure. While a façade is customarilyan elevation of a building, its appearing aspects do not alwaysaccord with the imagined wholeness of the architectural struc-tures they are associated with. When we go across a city, wemostly look at elevations, and we see through them buildings,which we also imagine to be buzzing with activities andenclosing variegated spatial interiors. Our perceptual experi-ence in immediate vision is in most cases supplemented byimaginary aspects that virtually constitute the plenitude of theform of what is seen.15

V

Although we may distinguish authentic qua proper appear-ances (namely those which relate to a strict act of seeing wherethe sides of the visible object are perceived in immediateintuition and direct vision) from inauthentic qua imaginedappearances (namely those which designate the surplus thataccompanies the authentic appearances in the constitutiveperception of the object of vision in its totality), perception isnevertheless not a mere act of double presentation, nor is it apure mode of correspondence between a content of conscious-ness and its real object.16 The full silhouette of a thing is

15 Although these supplements might occasionally surround things with fuzzydaydreams, perception sustains the sense of reality through vibrant experientialbodily displacements.

16 In phenomenological terms, a noetic activity (namely, the ‘‘intentionalactivity of consciousness’’ ) relates to the noematic correlate of an object (namely,the ‘‘objectively intended object of cognition’’ or the ‘‘intentional correlate’’).Given that every object is an intentional object, noesis designates the intentionalact while noema refers to the intentional correlate or objectively intended objectof this intentional act; namely, the intentional contents of the noetic acts. Thuswe intend objects through the noemata. In view of elucidating this noetic-noematicstructure, see: Edmund Husserl, Logische Untersuchungen. Erster Band: Prolego-mena zur reinen Logik, in Husserliana XVIII, ed. Elmar Holenstein (The Hague,1975); Edmund Husserl, Logische Untersuchungen. Zweiter Band: Untersuchungenzur Phänomenologie und Theorie der Erkenntnis, in Husserliana XIX, ed. Ursula

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constituted in motion by way of verifying the essential unitybetween its authentic and inauthentic appearances. Perspec-tive is essentially a phenomenon of the mystery of depth, whichdemarcates my situation in the world as being distinct fromthat of other perceivers; and yet, it is through spatial depth andits horizons that relations with others and things are openedup. Nonetheless, the fixity of the viewing and vanishingpoints in geometrical perspective is in sharp contrast with thevibrancy of the gaze in vision.17 Spatiality, which itself appearsthrough the kinesthetic movements of the human body, showsthat our embodiment grounds what we trust as being anevidentia perceptionis. In all of this, the iudicium sensus, thejudgment of sense, engages a process of learning.18

Space-time, depth and place, as well as the corporeal engage-ment of the observer within the spectacle, all ground percep-tion and its veridical potentials. It is through movement thatthe partial self-givenness of the formal reality of what is seenis a$rmed in its wholeness. In most cases, we look at thespectacle with trust, and we rightly do so when confrontingmost objects of vision; though it is likely the case that opticalillusions occur, and that camouflage as well as mimetic instal-lations might potentially mislead judgments associated withvision. And yet, perceptions are themselves a$rmed by othercomplementary verifying perceptions, whereby errors in visionget corrected by way of acuity and sensitivity in vision, ratherthan doing away with the epistemic possibilities that thispowerful human capacity o#ers to cognition.19

Panzer (The Hague, 1984); Edmund Husserl, Ding und Raum, in Husserliana XVI,ed. Ulrich Claesges (The Hague, 1973), sections 16, 24; Rudolf Bernet, Iso Kern,Eduard Marbach (eds.), An Introduction to Husserlian Phenomenology (Evanston,1995), pp. 116–17; Kevin Mulligan, ‘Perception’, in Barry Smith and DavidWoodru# Smith (eds.), The Cambridge Companion to Husserl (Cambridge, 1998),pp. 192–4; same volume: David W. Smith, ‘Mind and body’, pp. 323–93.

17 We could well state that: le regard ne cesse de vibrer; see: Cléro, Théorie de laperception, pp. 37–41, 46, 151.

18 A clear instance of this matter is shown in the manner visual artists andarchitects are pedagogically instructed and trained to develop acute skills indiscriminating seeing, as well as in studying and judging plastic forms andcolours in the built environment, in nature, in statuary and pictorial representa-tions, together with the generation of design directives.

19 It is perhaps the case that the stationary gaze of Descartes on objects ofvision might have led him to distrust the veridical conditions of sense perceptionas delineated in his Meditationes de prima philosophiae (1641–2 C.E.). It is alsoworthy stating herein that Alhazen’s account of the normal conditions of sightinvolved the following parameters: 1- The viewed object must be bright; 2- the


VI

Imagination (al-takhayyul; ��) played a pivotal role inAlhazen’s approach to the doctrine of the abstraction of the��. For instance, he advanced a physical model thatconsisted of a very fine thread held at high tension in view ofillustrating the quality of a geometric straight line, and inaiding imagination to constitute the subtlety of its trace,without implying in this that such mathematical entity existedin exteriority (bi-al-kharij). Alhazen posited a distinction be-tween �� and sensible entities, in view of securing anabstract domain for geometry that is not encumbered in itsdemonstrations by sensory constraints. Imagination, as an actof thinking, which describes an intellectual visualisation thatpartly rests on the traces shown by sensible entities whileappealing to common sense, o#ered Alhazen a conceptualplateau to establish his mathematical abstractions and toguarantee their invariance as idealities. As Rashed noted,Alhazen’s account of imagination carried with it some noeso-logical (in reference to noesis) and ontological bearings.20 Afterall, Alhazen believed that existents are of two principalclasses: sensible beings (those given by way of al-h*iss),and entities that exist in imagination and discernment(al-takhayyul wa-al-tamyız). He moreover held that the latterclass exists verily by way of an ascertaining tah*qıq (certifica-tio). For, he believed that the perception of sensible entities isprone to error and cannot be readily trusted in its veracity. Hefurthermore held that the sensible does not exist in truth andreality (laysa huwa mawjud ‘ala al-h*aqıqa), and that it iscorruptible, continuously changing and unstable, while the

distance between the object and the eye should be optimal (not too close and not toofar); 3- the object should be in a plane with the eye; 4- the body of the object shouldhave a proper volume; 5- if the body is transparent it should still allow for thetrapping of some light rays; 6- a completely transparent body that does not trap anylight rays is virtually invisible; 7- the distance between the viewer and the viewedshould comprise a transparent space; 8- the viewer should have sufficient time toview the object; 9- the eye should be healthy; 10- the eye should be able toconcentrate on an object (Kitab al-Manaz*ir, I.2 [1–26], I.8 [1–11]).

20 For an illuminating explication of the role of imagination in mathematics, andparticularly in reference to what Alhazen advanced in his tract Fı h*all shukukKitab Uqlıdis fı al-Us*ul, I refer the reader to: Roshdi Rashed, Les mathématiquesinfinitésimales du IXe au XIe siècle, volume IV: Ibn al-Haytham, méthodes géo-métriques, transformations ponctuelles et philosophie des mathématiques (London,2002), pp. 8–10.

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form that occurs in imagination is grasped according to itstruth, and does not continuously change with the variation ofwhomsoever imagines it (al-s*ura allatı tah*s*ul fı al-takhayyul‘ala h*aqıqatiha wa-laysat tastah* ıl wa-la tataghayyar bi-taghayyur al-mutakhayyil laha). Ultimately, this line in think-ing gave primacy to imagination over sensation, as well asrevealed the mathematical idealities as being invariable, dis-tinct and intellective forms that exist independently of thesubject who thinks them.

The imagined aspects of a visible object supplement thecontinuum of its manifold appearances, as well as structure itsplenitude as a thing that is seen in its totality by way ofspatial-temporal displacement. As Alhazen asserted, visualperception by way of contemplation and recognition involvedmovement as well as an insensible lapsing of time (Kitabal-Manaz*ir, II.4 [20, 26]).21 However, as we have highlightedabove, the act of imagining approximates the physicality of thevisible thing by way of an imagined form that is measuredagainst a forma universalis in view of grasping its forma vera inexperiential presence (Kitab al-Manaz*ir, II.4 [22–35]).

In perception, things are surrounded by the imaginary(l’imaginaire), which projects their virtual wholeness as aphenomenon of structure for their visible aspects. Vision seemsto be a process that pertains to fiction as well as reality inpointing to modes by which essences get revealed. Whilethe geometrician makes recourse to imagination, the very actof seeing is itself imbued with imagining, not only in the face ofthe miniscule or the colossal, which overcome the horizons ofour everyday perceptions, but precisely with most things thatwe discern and compare in seeing. Moreover, in contemplatingbeings in nature, imagination may generate an aesthetic sense,which translates itself into a feeling of beauty (when imagina-tion accords with understanding) and points to the cipher ofnature that announces a finality without ends (as if evokingthe Greek conception of �� ). Yet, a feeling of thesublime also arises when the productive imagination is over-stretched to its furthest limits in its attempt to estimate themagnitude of colossal and mighty natural phenomena. Thepower of the limitless in nature confronts the imagination with

21 The role of time in visual perception is elucidated in: Kitab al-Manaz*ir, II.3[57–66].


the non-comparative magnum. Overstrained, the imagination,which is a requisite for empirical cognition, cannot estimatewith adequacy the extent of the mathematically sublime withwhich all else is radically small and whose concept is too vastfor presentation.22

Memoria (al-dhikr or al-tadhakkur) this grand force of life,which is at work in reference to vision, recognition andimagination (Kitab al-Manaz*ir, II.3 [19–20, 24–25], II.4 [13–15,22]), gathers and reproduces numerous images and experi-ences, ranging from the properties of sensuous objects to thoseof mathematical entities. However, memoria seems also to beclosely associated with oblivio as absence, whereby forgetful-ness points to a search for remembrance. Discernere (al-tamyız), which is a scrutinizing act of di#erentiation, is also amode of colligere (recollection) in the sense that it is agathering of what has been retained by memoria. Discernere isthus a meminisse as well as cogitare. It is a manner by which themanifold is classified, recollected and identified under speciesthat orient perception in the dispersion of the appearances.However, based on the becoming of things and their change intime, Alhazen argued that prior knowledge, comparativemeasure, imagination and memory, do not decisively securethe veracity of what is seen, nor do they warrant an access tothe true form of things without a scrutinising engagementin the re-verification of the reality of what appears, andan experiential re-inspection of its visible aspects (Kitabal-Manaz*ir, II.4 [29–35]).

The visible properties of things, which in geometrical andphysical terms describe an invariance in their presence, displayperceptual variations in perspective in terms of the angle anddistance under which they are seen, along with their orienta-tion, the reflection of light on their surfaces, the intensity oftheir brightness, the vibrancy of their colours, the levels ofcontrast in the delineation of their outlines, and the visualestimation of their apparent sizes. However, the object ofvision is itself grasped as a facies totius universi that

22 The rise of a feeling of the sublime in the overstraining of the capacities ofthe imagination was intricately elucidated in Book II on the ‘Analytic of theSublime’ in Kant’s Critique of Aesthetic Judgment, trans. James Creed Meredith(Oxford, 1911).

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is unchangeable,23 and it appears as a constant �� (presence) despite its optical variations in perspective. Seeingdoes partly let things self-show themselves as they are. For,what appears in the spectacle is led back to an order offamiliarity, and seeing is a mode of recognition that lets whatappears self-show itself as it is given in its own apparition inpresencing. However, the semblance of constancy in presence isnot guaranteed after the lapsing of a considerable period oftime given that things are subject to becoming and change(al-taghayyur; alteratio or mutatio). Observing this state ofa#airs led Alhazen to reinforce his belief that a concreteverification of the apparent reality of things has to beexercised, given that prior knowledge and recollection do notsu$ce in certifying and ascertaining the approximated trueform of what is seen (Kitab al-Manaz*ir, II.4 [29–35]).

VII

Following phenomenological directives, we note that some-thing lets itself be brought to light or brightness in its appear-ing, and self-shows itself from itself in that very condition ofbeing lit. This event describes the unfurling of what may bereferred to as apophainesthai ta phainomena, namely, whatshows itself from itself, just as it shows itself from itself. It isultimately a translation of the maxim that animates phenom-enology by the calling: zu den Sachen selbst (to the thingsthemselves). And, phenomenology is conceived herein as afundamental ontology (Fundamentalontologie) that elucidatesthe question of being (Seinsfrage) by way of a hermeneutic aswell as eidetic reflection on what is pointed at by the appella-tions: �� (bringing beings to light or brightness), ��(showing itself from itself), and �� (what self-showsitself from itself).24

The thrust of Alhazen’s theory of visual perception implicitlypoints to the possibilities of grasping optics not merely as a

23 Regarding this matter, see: Maurice Merleau-Ponty, Phénoménologie de laperception (Paris, 1945), pp. 346–7.

24 See: Martin Heidegger, Sein und Zeit, Gesamtausgabe 2 (Tübingen, 1953),section 7. In other terms, the phenomenon becomes indicative of itself, wherebyappearance does not conceal the essence of a thing as much as reveal it; if noteven letting essence become self-shown as an apparition. Refer also to: Jean-PaulSartre, L’être et le néant, essai d’ontologie phénoménologique (Paris, 1943), pp. 11–16.


discipline that inquires about the conditions of sight and lightin terms of an epistemology of photosensitive surfaces, butmoreover as an eidetic inquiry about the geometric constitu-tion of forms in their essential ordering structures that isgrounded by experiential verifications. If one were to endeav-our to elucidate the question of being based on Alhazen’sgeometric optics, the resulting discipline will not readily bethat of a surface-ontology but more likely a line of inquiry thatelucidates the presencing of beings.

Vision is a mode of de-distancing that brings things that arenot at hand nearer from their remoteness, and renders beingsaccessible even from afar. Linear perspective, and its pictorialorder, does itself demarcate a distance between the eye of theobserver and the objects of vision; yet, it de-distances beingsin sight by assimilating the seen spectacle in the form of apicture. However, the distances or intervals that are clearedby vision, and that are accordingly brought into nearness inde-distancing, are not objective or measurable as such. Rather,they are existentially estimated in the very circumspect actof seeing as a spatial mode of encountering beings inde-distancing.

As Alhazen highlighted, in order that the distance whichseparates the observer from the object of vision gets estimated,the thing being perceived ought to be near objects that areordered and contiguous (ajsam murattaba wa-muttas*ila; cor-pora ordinata et continua – Kitab al-Manaz*ir, II.3 [76–80]), aswell as share a common terrain with the observer. To demon-strate the manner by which this situational condition needs toobtain in order that a successful approximation of the esti-mated distance and apparent size of an object can be achieved,Alhazen described an experimental installation that consistedof a wall W (h*a’it*) dividing a space S (fad*a’ or bayt) into twodistinct parts A and B, which were not visually linked butthrough a pinhole aperture p (thuqb), located in the wall W, insuch a way that the floor F (wajh al-ard* ) of the space S couldnot be seen when looking through it. Part A of the space Sreceived objects that could only be viewed from part B of thespace S through the aperture p (granted that observers situ-ated in B did not know what was in A prior to looking throughp). Then, two screens s1 and s2 (jidaran), were introduced intopart A, at distances d1 and d2 from the dividing wall W, such asd1>d2, and whereby s2 concealed a part of s1. Standing in part

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B, and looking through the aperture p into part A, theobservers in that experiment could not detect the di#erencebetween the distances d1 and d2 of the screens s1 and s2, letalone estimate that d1>d2. Moreover, when the two screenswere subjected to an intense light, the observers were hardlyable to distinguish them from each other. Alhazen evoked asimilar experiment using a rope r (h*abl) and a bar b ( ‘ud), eachbeing respectively placed in the face of the aperture p atvarying distances from the wall W, and observers could notestimate the distance that separated these objects from Waccurately (Kitab al-Manaz*ir, II.3 [80–84]). In reinforcing theseobservations, Alhazen asserted that the innate (al-fit*ra), habitor custom (al-‘ada, or al-ma’luf), the acquired (al-iktisab), theknown (al-ma‘ruf), analogy (al-tashbıh), and al-tamyız wa-al-qiyas, all contribute to the estimation of distances and theirmagnitudes including the sense of depth (Kitab al-Manaz*ir, II.3[135–161]). Moreover, the common ground or terrain, to beshared between the observer and the object of vision, is itselfdetermined in reference to the body of the observer, wherebythe feet (al-qadamayn) in pacing, the stretched forearm(dhira‘ ) and hand (yad) in grasping, as well as the scale of thehuman body (al-qama) all act as measure determinants in apre-reflexive and non-intentional manner (tataqaddar bi-jismal-insan bi-ghayr qas*d; Kitab al-Manaz*ir, II.3 [150–155]).25 Inaddition, Alhazen highlighted that perception occurs fı aqallal-qalıl min al-zaman (Kitab al-Manaz*ir, II.3 [100]), and thatdiscernment and comparative inferential measure happen fızaman fı ghayat al-s*ighar (Kitab al-Manaz*ir, II.3 [26–27]).Furthermore, he noted that the sensation (ih*sas) which takesplace in the eyes resembles other forms of sensation in refer-ence to the workings of the brain, including tangible ones(al-malmusat; Kitab al-Manaz*ir, I.6 [80]). The tactile cumbodily properties seem herein to be entangled with the visual

25 It was customary that the measuring of distance drew on the human bodyand its scale. This was the case with practices of linear measurement ingeography, cartography and surveying, as well as in cadastral and fiscalmanagement of agricultural land and the establishment of architecturalstructures. The human bodily limbs were also set as small-scale determinants inmeasuring clothing, furniture, and decorative features. The finger (is*ba‘ ), theforearm (dhira‘ ), the distance from fingertip to another (shibr), the feet(al-qadamayn) were indicative of this practice. The bodily experience also actedas a scale-setter of the distance that a traveler covers as implied by ��or mille passus (al-mıl).


ones, whereby objects almost appear as �� that aregathered in ��, and where the visual space seems to be anirreducible manual space.26

The estimation of the actual size (al-‘iz*am) of distinct objectsthat have di#ering magnitudes cannot be solely based on theangle of the virtual cone of vision (zawiyat makhrut* al-shu‘a‘ )within which they are seen. For the same visual angle maysubtend or group two objects that are equal in size, which areat equal distances in facing the observer, as well as two otherobjects that are unequal in scale, which are positioned atdi#ering distances from the observer. The distance between anobserver and a visible object is as significant in the estimationof the object’s actual scale as the angle of vision under whichit appears (Kitab al-Manaz*ir, II.3 [144, 147–148]). The visualangle generated in the appearing of an object of vision is to beaccounted for in conjunction with the distance of this objectfrom the eyes of the observer; namely its situation in depth.After all, it is clearly not the case that the larger the angle ofvision, the greater is the size of the object under which it isseen. For a small object placed relatively near to the eyeswould as well be seen at an angle having the same value as theone generated in seeing a much larger object at a furtherdistance away from the observer. This matter is a$rmed inAlhazen’s rejection of the explication of the estimation ofthe size of a given object of vision by way of solely relying onthe degree of the angle of the visual-ray pyramid / cone underwhich it is seen, as advanced in the conjectural models ofthe mathematicians (as*h*ab al-ta‘alım; mathematici – Kitabal-Manaz*ir, II.3, [135–140, 161, 168]).

Even with the presence of ordered contiguous objects atproximity of a given thing X, and the existence of a commonterrain that is shared between the observer and that thing X,the estimation of the actual size of X based on its apparent sizemight not always be achieved by way of unaided visual percep-tion, and it remains to be a mere act of approximation. Incircumstances that require a relative degree of exactness inestimating distances, Alhazen resorts to geometrical methodsof measurement. For instance, he devised practical steps toperfect measurement by placing geometry as the theoretical

26 We are not implying here that Alhazen’s account of visual perceptioninvolves subjective embodiment, given that such notion was not systematicallydeveloped but through post-Kantian conceptions of subjectivity.

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foundation of the applied science of surveying ( ‘ilm al-misah*a).27 Other ocular circumstances may also not enable ourunaided perception to explain certain visual events, like it isthe case with the moon illusion.28 For, based on actual obser-vations, the moon looks in certain nocturnal situations asbeing greater in size at the horizon than it does at its culmina-tion; a variation that shakes the sense of constancy in scaling.In his tract On the Appearance of the Stars (Fı ru’yat al-kawakib) Alhazen’s explication of this phenomenon of appar-ent magnification advanced refraction as an accidental causeof the illusion via non-rectilinear vision, which in certainconditions resulted from a thickening of vapour in the terres-trial atmosphere.29 The change in the moon’s apparent size alsopartly depends on modifications in the cues of distance; since,against the horizon, the moon looks larger due to its associ-ation with a greater sense of depth. Moreover, the estimation ofthe size of visible objects may su#er from the deceiving errorsin vision (aghlat* al-bas*ar; deceptionis visus), like when anobject that is exceedingly far from the observer (namely fallingoutside a moderate range) is assumed under an extremely smallangle of the cone of vision, the magnitude of this object may bejudged as being smaller than what it is (For, sight errs ininference and recognition when the position of an object fallsoutside the range of moderateness; Kitab al-Manaz*ir, III.7[8–9]).

VIII

In his Risala fı al-makan (Treatise on Place),30 Alhazen arguedthat place (al-makan) consisted of the imagined and invariabledistances of the containing body, which are devoid of matter,

27 This geometrical demonstration is advanced in reference to Alhazen’sendeavour Fı al-misah*a in: Roshdi Rashed, ‘Les mathématiques de la terre’, inGiancarlo Marchetti, Orsola Rignani and Valeria Sorge (eds.), Ratio etsuperstitio, Essays in Honor of Graziella Federici Vescovini, Textes et études duMoyen Âge, 24 (Louvain-la-Neuve, 2003), pp. 285-318, pp. 286–90.

28 Abdelhamid I. Sabra, ‘Psychology versus mathematics: Ptolemy and Alhazenon the moon illusion’, in Edward Grant and John E. Murdoch (eds.), Mathematicsand its Application to Science and Natural Philosophy in the Middle, Essays inHonor of Marshall Clagett (Cambridge, 1987), pp. 217–48; Abdelhamid I. Sabra,Optics, Astronomy and Logic (Aldershot, 1994), chapter IX.

29 Sabra, ‘Psychology versus mathematics’, section II.30 An Arabic critical edition and annotated French translation of this epistle is

published in: Rashed, Les mathématiques infinitésimales, IV, pp. 666–85.


equal to what is contained, and having a figure that resembledit (al-ab‘ad [al-thabita al-mutakhayyala] allatı qad int*abaqat‘alayha ab‘ad al-jism wa-ittah*adat biha).31 The mode of being ofplace, namely its existence, is established in the imagination,which constitutes invariable mathematical entities.32 Place(al-makan) as the imagined void (al-khala’ al-mutakhayyal)appears as a spatium imaginatum, which points to a thesis thatwas partly inspired by the arguments of the grammarian JohnPhiloponus (6th cent. C.E.),33 and that furthermore carriedsome resonance with what was echoed later in the works ofGalileo, Descartes and Newton, in their respective critiques ofAristotle’s definition of � � as the innermost motionlesssurface of the containing body that is in contact with what itcontains (�¢´�� ’�� , �’’�� ¢ � �; Physics, IV 212 a 20–21).34 Alhazen’s geo-metrisation of place was itself radically questioned by thephilosopher ‘Abd al-Lat*ıf al-Baghdadı (d. circa 1231 C.E.) inhis epistle: Fı al-radd ‘ala Ibn al-Haytham fı al-makan (ARefutation of Alhazen’s Place),35 which was drafted in defenceof Aristotle’s thesis. Although Alhazen’s makan exists in animaginary plateau, like other geometrical entities, it is unclearwhether this mode of existing resolves the ontological questionof space, given that we are confronted herein with a distinctionbetween the imagined mathematical entity and the concreteexistence of a physical being externally (fı al-kharij). Andyet, the mathematical conception of place is analogicallyconstructed with respect to the concreteness of the sensible

31 Rashed, Les mathématiques infinitésimales, IV, pp. 677, 4. As Rashed alsohighlights in that context (ibid, p. 662, n. 25), echoes of this definition are foundin Descartes’ Discours de la méthode, wherein it is stated: ‘‘l’objet des géomètres,que je concevais comme un corps continu, ou un espace étendu en longueur, largeuret hauteur ou profondeur, divisible en diverses parties, qui pouvaient avoir diversesfigures et grandeurs, et êtres mues ou transposées en toutes sortes’’ (Œuvres deDescartes, ed. Charles Adam and Paul Tannery [Paris, 1965], vol. IV, p. 36).

32 Rashed, Les mathématiques infinitésimales, IV, pp. 8–9, 660.33 Philoponus attacked Aristotle’s definition of topos, and argued that place is

an immobile three-dimensional extension that is conceivable as void, withoutentailing that it is ever empty in fact. See: John Philoponus, Corollaries on Placeand Void, trans. David Furley (London, 1991); Ioannis Philoponi in AristotelisPhysicorum libros quinque posteriores commentaria, ed. Hieronymus Vitelli, Com-mentaria in Aristotelem Graeca XVII (Berlin, 1888); Rashed, Les mathématiquesinfinitésimales, IV, pp. 655–62.

34 Aristotle, Physics, ed. William David Ross (Oxford, 1950).35 An Arabic critical edition and annotated French translation of al-Baghdadı’s

tract is published in: Rashed, Les mathématiques infinitésimales, IV, pp. 907–53.

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presence of container and contained.36 This state of a#airstacitly refers us back to the topological dimensions ofAlhazen’s theory of visual perception as they were determinedby his a$rmation of the visibility of depth (al-‘umq; profun-dum; �� ), which, as a distance (al-bu‘d; distantia; ��)between the organ of vision and its objects, designates aninterval (al-masafa; intervallum or spatium) that carriesa certain magnitude (miqdar), and is one of al-ma‘anıal-mubs*ara.37

The significance of Alhazen’s a$rmation of the visibility ofdepth (principally in reference to al-bu‘d, al-wad*‘ and al-tajassum; Kitab al-Manaz*ir, II.3 [67–126]) acquires furtherphilosophical momentum when contrasted with the immateri-alist doctrine of the Bishop of Cloyne, George Berkeley (d. 1753C.E.), who attempted to reject this phenomenon (namely, theperceptibility of depth),38 and who was eventually criticallyinterrogated by Merleau-Ponty specifically in reference to thisthesis.39 We are hence facing herein, three of the finest thinkers(Alhazen, Berkeley, Merleau-Ponty), separated by history, cul-ture, language, and philosophical-mathematical penchant,each struggling in his own right to solve a common problemthat continues hitherto to point to the mystery of depth and tothe ontological question of space.40

36 See: Khalid Bouzoubaâ Fennane, ‘Réflexions sur le principe de continuité àpartir du commentaire d’Ibn al-Haytham sur la proposition I.7 des Élémentsd’Euclide’, Arabic Sciences and Philosophy, 13 (2003): 101–36, p. 122.

37 See also: Alhazen, Dubitationes in Ptolemaeum (al-Shukuk ‘ala Bat*lamyus),ed. A. Sabra and N. Shehaby (Cairo, 1971); Alhazen, Dubitationes in Ptolemaeum,trans. Abdelhamid I. Sabra, Journal of the History of Philosophy, 4 (1966): 145–59.

38 Refer to Berkeley’s views in: sections 2–28 and 41–51 of An Essay Towards aNew Theory of Vision (1709 C.E.); sections 43–44 of A Treatise Concerning thePrinciples of Human Knowledge (1710 C.E.); the first dialogue in Three DialoguesBetween Hylas and Philonous (1713 C.E.), along with remarks in The Theory ofVision Vindicated and Explained (1733 C.E.). See also: The Works of GeorgeBerkeley, Bishop of Cloyne, eds. Arthur A. Luce and Thomas E. Jessop, 9 vols.(Edinburgh, 1948–1957); George Berkeley, Berkeley’s Philosophical Writings, ed.David M. Armstrong (New York, 1965).

39 See Merleau-Ponty, Phénoménologie de la perception, pp. 294–309. Alsoconsult: Joseph J. Kockelmans, ‘Merleau-Ponty on space perception and space’,in Joseph J. Kockelmans and Theodore J. Kisiel (eds.), Phenomenology and theNatural Sciences (Evanston, 1970), pp. 281–96.

40 I have considered this ontological question elsewhere; see: Nader El-Bizri,‘Qui êtes-vous X�PA: On receiving Plato’s Timaeus’, Existentia Meletai-Sophias,XI (2001): 473–90; Nader El-Bizri, ‘A phenomenological approach to theontological question of space’, Existentia Meletai-Sophias, XII (2002): 345–64;Nader El-Bizri, ‘ON KAI X�PA: Situating Heidegger between the Sophist and the


Berkeley believed that the distance out from the eye cannotbe immediately perceived but can only be suggested by mentalcues o#ered to vision.41 In the first dialogue, Philonous, themind-lover defending Berkeley’s doctrine, stated that sightdoes not show or in any way inform us that the visual object,which we immediately perceive, exists at a distance, given thatobjects produce two-dimensional projections on the retina, andin consequence, there cannot be an immediate vision of three-dimensionality. Hence, depth cannot be perceived, but is sim-ply experienced; and so is the case with the estimation of thesize of objects at a remote distance. Relying on the convergenceof the eyes in judging the cues of the apparent size of an objectof vision, Berkeley evokes the angle of vision as the princi-pal estimative determinant, following in this the classicalmathematicians, which, as noted earlier, were criticallyinterrogated by Alhazen on this question.

If distance cannot of itself be seen without the mediation ofwhat is other than itself, then the mind, which does notimmediately perceive the idea of distance of itself, must do soby the means of another idea. A conceptual perplexity ariseswhen we hold that distance, which is imperceptible due to itsown nature, is nonetheless grasped by sight. What this entails,is that it is sensed by the mediation of another idea that isimmediately perceptible.42 The lines, angles, and projections,used by those who master the art of perspective and theanalytical tools of geometry, constitute of themselves sets ofideas that render the process of vision explicative. However,Berkeley does not see them as being grounded on experience,given that they are posited as abstract ideas. On his view, thescience of optics and the art of perspective do not adequatelycontribute to the elucidation of the perception of distancegiven that their ideas are not of themselves immediatelyperceived in vision. Being themselves imperceptibles, theseideas do not assist the mind in judging distance or depth, giventhat their lines and angles are non-existent abstract constructs

Timaeus’, Studia Phaenomenologica IV (2004): 73–98; Nader El-Bizri, ‘Ontopoièsisand the interpretation of Plato’s Khôra’, Analecta Husserliana, LXXXIII (2004):25–45. See also: El-Bizri, ‘La perception de la profondeur: Alhazen, Berkeley etMerleau-Ponty’; El-Bizri, ‘La phénoménologie et l’optique géométrique’.

41 Berkeley, Theory of Vision, section 2.42 Berkeley, Theory of Vision, sections 9–11.

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introduced by mathematicians into the field of optics.43

Mediaeval scholars of the calibre of Alhazen, Roger Bacon,Witelo, and John Pecham,44 would have been indirectlytargeted by Berkeley’s critique of ‘‘the misled writers of optics’’who ‘‘confusingly’’ take the act of judging distance as if it weresimilar to that of drawing a conclusion in mathematics.45

Berkeley’s disdain of mathematical pointers and demonstra-tions is ultimately attributable to his rejection of the veracityof abstract ideas that have ‘‘no experiential ground’’.

Using Berkeley’s parlance, the experiential connectionbetween the idea of distance, the idea of sensation, and the ideaof ocular disposition, is said to be habitual. Consequently, theidea of distance is perceivable by means of another idea that isimmediately perceived; namely, the corresponding sensationarising from the dispositional turn of the eyes and theirconvergence as suggested to the mind.46 However, the idea ofdistance is perceived by the ear as well as the eye, and yet, theidea suggested by hearing is di#erent from that suggested bysight, and the visible, the audible,47 as well as the tangible, arenot the same object; although they seem to be convergentexperientially.48 According to Berkeley, these classes of ideas

43 Berkeley, Theory of Vision, sections 11–15.44 Regarding representative Latin texts within the perspectivae tradition in

mediaeval science, see: Roger Bacon, The Opus Majus, trans. Robert Belle Burke(New York, 1962); Roger Bacon, Opus maius, ed. John Henry Bridges, 3 vols.(Oxford, 1900); Roger Bacon, De multiplicatione specierum, ed. David C. Lindberg(Oxford, 1983); Witelo, Witelonis perspectiva liber quintus, trans. by Albert MarkSmith (Wisconsin-Madison, 1976); John Pecham, Perspectiva communis, ed. andtrans. David C. Lindberg (Wisconsin-Madison, 1970); John Pecham, Tractatus DePerspectiva, ed. David C. Lindberg (New York, 1972).

45 Berkeley, Theory of Vision, section 24.46 Berkeley, Theory of Vision, sections 16–20.47 It is worthy noting herein that Alhazen evoked the role of the audible

(al-masmu‘at) in reference to the perception of position (idrak al-wad*‘ ); see:Kitab al-Manaz*ir, II.3 [98].

48 Berkeley, Theory of Vision, sections 47–9. A parallel phenomenon points toMerleau-Ponty’s interpretation of the Hannover Institute experiment on visionwhereby a subject is fitted with special goggles equipped with lenses that invertthe objects of sight by way of redressing the retinal images. Initially, theexperimental subject notices that the visible and the tactile are disparate, as ifthey did not have the same perceptual and spatial field of reference. However,after a short period of ocular adjustment, visible objects are redressed and appearto be in synchrony with their tactile dispositions, even though the lenses fitted onthe goggles would still redress the retinal images. After removing the goggles, thesubject experiences visual disorientation, wherein the spectacle appears asinverted, even though the retinal images are themselves in inversion. And yet,after a period of correction, the normal conditions of sight are restored. This


(which get intertwined and incorporated in one another)reinforce the prejudice of our thought and confuse our use oflanguage. Ultimately, the idea of a thing that we immediatelyperceive neither sense nor reason informs us that it actuallyexists without the mind.49 Berkeley’s immaterialist hypothesisentails that physical objects cannot exist unperceived;whereby, existence is percipi, and it evokes a percipiens,wherein the objects of vision get reduced to ideas.50 However, itseems that Berkeley blurred the distinction between the senseperceptions of a physical object and its proper sensible quali-ties. He moreover seems to have confused perception withthinking, by grouping mental images with sense perceptions,and refusing to draw a distinction between primary and sec-ondary qualities. In addition, he rejected the idea of there beinga substratum that supports our perceptions and gathers themaround a being. Based on his thesis, a talk about thingsthemselves becomes a confusing jargon; and yet, the absurdityand untenable position that may result from this line inthinking does not show that what Berkeley claimed regardingphysical objects is not also applicable to the existence of otherminds.51

The philosophical thrust of a$rming the visibility of depthis best elucidated in Merleau-Ponty’s phenomenologicalapproach to the perception of space. Based on our experientialsituation in the world we are not granted the simultaneousimmediacy of seeing depth from our perspective as well asseeing it in profile from the position of a viewer who looks at itlaterally. However, this does not readily reduce the primacy ofdepth (la profondeur) into simply being a dimension likebreadth (une largeur); given that depth is the most existentialof all the dimensions, since it intrinsically belongs to ourhuman perspective, while breadth, length, height, and width,

phenomenon was seen by Merleau-Ponty as being indicative of our bodilyperceptual inherence in the world. See: Merleau-Ponty, Phénoménologie de laperception, pp. 284–6. I have also addressed this matter elsewhere in detail, see:El-Bizri, ‘A phenomenological approach to the ontological question of space’.

49 Berkeley, Dialogues, I, pp. 164–5.50 To better grasp Berkeley’s hypothesis, we are led back to his rejection of

John Locke’s Representative Theory, which was advanced in the latter’s EssayConcerning Human Understanding (ca. 1690 C.E.).

51 Berkeley advocated a theological ground for overcoming these conceptualobstacles by way of securing the existence of the All in terms of believing that itis perceived in simultaneity by the Divine All-Perceiving-Perceiver.

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belong to objects, or relations between things. It is depth thato#ers the self openness to the world. Even though it is whatemerges out of positing a subject, depth does nonetheless pointto an inter-subjective otherness. Perspective, the convergenceof the eyes, and the apparent sizes of the objects of vision, arenot signs or causes of depth; they are rather phenomena ofdepth that open up the unfurling self to the world and itsbeings. The convergent lines in perspective appear as parallellines from a phenomenal standpoint, and apparent sizes pointto their actual scale in depth. Nevertheless, although depth issaid to be a visible property, it is itself seen in a manner that isradically other than all distances. Being the ground of ourperspective on things, it furnishes us with a space of opennessto communicate with other minds by way of merging thehorizons of our fields of vision and sensory perception, alongwith associated exchanges of signifiers. It is ultimately thedimension by virtue of which things appear as enveloping oneanother rather than being juxtaposed. Unlike mathematicalrepresentations, depth highlights the manner reality impingeson us and confronts us with a sense of mystery in its eventfulpresentations.

IX

The discerning eye has been given a merited attention in thetheories of perception. Yet, this interest in investigating thecognitive and epistemic bearings of vision may have veiledthe dynamic workings of the desire of the eye. After all, visiondoes not only point to a curiosity for knowing; it is moreoveran aesthetic as well as tempting appetite for experiencingpleasure. An interest in vision does not always translate itselfinto an account of truth or falsity, but rather also cares forbeautiful looks, vanity, glowing colours and variegated shapesthat entice the senses. After all, Alhazen did not hesitate toshow how the visible properties of things, individually and incombinations, lead to a sense of beauty (al-h*usn), while placingan emphasis on proportionality (al-tanasub) and harmony incomposition as being significant aesthetic determinants (Kitabal-Manaz*ir, II.3, [200–231]).

As a mode of scrutiny, vision is seemingly posited as astate of thinking that we see. Like naming, seeing involves


signification, and is semantically and symbolically loaded.52

However, construing vision as an act of cognition does notreadily posit the �� (ruh* nafsanı) as a �� ’ �� (ruh* bas*ir), which, as a move that is inspired by aGalenic model of vision, grasps the truth of light as a cognitiveseeing. And yet, as we have highlighted above, Alhazen dis-tinguished the conditions of the propagation of light from thoseof vision, while retaining a mathematical model for explicatingvisual perception in terms of the sensory intromission of lightinto the eye.53

An insight into a line in thinking that may have alsoconverged seeing with knowing can be detected in comparativeterms by contemplating the meaning that is aimed at in thefirst proposition that opens Aristotle’s Metaphysics, namely:�� ’�� ’�� ’ �� (Metaphysics, A,980 a 21). This line is customarily translated as: All humans bynature desire to know;54 however, an alternative (yet polemical)reading proposes a German rendering as: Im Sein des Menschenliegt wesenhaft die Sorge des Sehens (The care for seeing isessential to the being of the human being).55 Herein, �’�� (toknow, to see) is grasped as being linked to �’y�� (outwardappearance, look) insofar that the latter is construed as beingthe visible form of something. Knowing is transmuted into anact of seeing, whereby ¢ �� (sight) brings about knowledge ofthings more e$ciently than all the other senses and is hencenot reducible to the order of mere sense perception. The

52 One could point in this context to the reflective structure of the verbum,which, like light, makes things visible, including itself (expressio exprimentis etexpressi); see: Hans-Georg Gadamer, Truth and Method, trans. revised by JoelWeinsheimer and Donald G. Marshall (London, 1989), p. 503.

53 We perhaps do not need to be reminded herein that Alhazen’s focus was onlight as d*aw’, whose nature and essence are physical, while its comportment ismathematically determinable. This state of a#airs accentuates Alhazen’sintellectual integrity, particularly when his Optics was composed in anintellectual and geo-cultural environment (Cairo, ca. post-1028 C.E.) dominatedby fat*imı doctrines that were imbued with metaphorical and onto-theologicalspeculations about the existential power of light (principally as al-nur). Inclassical forms, the distinction between lux and lumen, may also be found in thedouble sense of light which carries the names: �� and �� . For an insight intoAlhazen’s discussion of light, its form and essence, in a tract that is other thanhis Optics, I refer the reader to: Roshdi Rashed, ‘Le ‘‘Discours de la lumière’’d’Ibn al-Haytham (Alhazen). Traduction française critique’, Revue d’histoire dessciences, 21 (1968): 197–224; repr. in Optique et mathématiques, V.

54 Aristotle, Metaphysics, ed. David Ross (Oxford, 1924).55 Heidegger, Sein und Zeit, section 36.

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correspondence between knowledge and vision is perhaps alsoattested in the manner Plato reinforced the cognitive characterof �� over that of �’��; wherein vision shows ratherthan tells, and where orality gives way to the rise of literacy.56

In addition, and as noted by Aristotle, ¢ �� highlights thedi#erences between things (Metaphysics, A, 980 a 25), in this, itmay be seen as being akin to the etymological root of ��;whereby the Greek terms �� (spectacle) and ¢ �� (to see, tolook) are brought together in determining ��, which thusrefers to the act of seeing a spectacle, or looking at a view.57

However, one should not conclude that most of the workings ofseeing are theoretical. For, some scholars critically speculateabout the longstanding philosophical primacy of vision as amanner of access to beings.58 Although seeing as knowing wasmediated at varying levels by way of what the Greeks named:�’��, �’��, ��, �’��, � ��, � �� and � ��,the care for seeing does nonetheless intersect with a desire toknow. Both find their roots in curiosity, and in the modernadvent of Die Zeit des Weltbildes, whereby �� becomes arepresentational mode of seeing, with the human subject turn-ing into the grounding Archimedean vantage point.59 In this,the observer is not a passive receptor of visual stimuli, but israther an engaged spectator with a stance and posture towardswhat appears, by way of standing within the site that allows forthe glance of the eye (Augenblick) to en-frame the world inpicturing it.60

As a private subjective a#air, seeing, which is captivatedwithin perspectives, was translated into an inter-subjectivephenomenon by way of the geometrisation of the eye and the

56 See: Gerald A. Press, ‘Knowledge as vision in Plato’s Dialogues’, TheJournal of Neoplatonic Studies, 3 (1995): 61–89.

57 See: Martin Heidegger, Vorträge und Aufsätze (Pfüllingen, 1985), p. 48;William McNeill, The Glance of the Eye: Heidegger, Aristotle, and the Ends ofHistory (Albany, 1999), p. 174. The insight pointed at in this context may itselfaccord with the interrelations of the family of Arabic terms: naz*ar, naz*ariyya,manaz*ir, and manz*ur, which respectively designate: seeing, theory, optics,perspective or the seen.

58 McNeill, The Glance of the Eye, pp. x–xi.59 McNeill, The Glance of the Eye, p. 221.60 For instance, in a$nity with a humanist spirit, Alberti adopted a

‘‘Christianized version’’ of Protagoras’ maxim: Hominem [inquiens] modum etmensuram rerum omnium esse, namely: �� ’�� (That the humanbeing is the scale and measure of all things); Leon Battista Alberti, De Pictura etDe Statua, ed. with trans. by Cecil Grayson (London, 1972), I.18.


resultant emergence of a structuring model of perception thatis determined by mathematical perspective. This matterbecame most sharply highlighted in the views of the masters ofthe perspectivae tradition in the history of Renaissance art andarchitecture.61 This pictorial representational quest was partlyanimated by a desire of mathematisation, and the founding ofoptimal geometric constructions, which eventually restrictedthe autonomy of painters from depicting a spectacle accordingto the privacy of their intimate perceptual experiences. Thepainter was thus obliged to study the art of geometry, if notalso grasp the rudimentary principles of optics. A theory ofart was henceforth in the making. Although the spread of amathesis universalis spirit was hardly hidden in art and archi-tecture, perspective was nonetheless an expression of a deepdesire for depth (un désir de profondeur). This state of a#airs isillustrated in the manner a painting appears as a focus imagi-narius that entices the observer to become emplaced in thespectacle that is depicted, which is accordingly supplementedwith imagined sensory experiences that overcome its pictorialspatiometric and chronometric limitations.62 The viewer is thusinvited to imaginatively inhabit the artwork. Although inpainting (tazwıq), the chromatic variations, the use of outlines,and the contrast in colour, all assist in generating an illusionof depth and texture (Kitab al-Manaz*ir, III.7 [40–43]), thedesire to generate a sense of depth does not simply aim atcommunicating a lived experience, as much as it ultimatelyintegrates a geometrical impetus in structuring pictorial per-spectives. This longstanding mathematical drive, and its matu-ration in the unfolding of the essence of techno-science, ledsome contemporary cultural theorists to connect the founda-tions of modern architecture with the history of science.63

61 See: Alberti, De Pictura et De Statua; Lorenzo Ghiberti, Commentarii(Napoli, 1947); Piero della Francesca, De prospectiva pingendi, ed. GiustaNicco-Fasola (Firenze, 1989).

62 Special visual e#ects can be generated in two-dimensional pictorial represen-tations that defy the geometric structure associated with concrete three-dimensional physical solids. It is possible in two-dimensional graphic media toestablish suggested spatial configurations that cannot be built in actual materialforms. The drawings of M. C. Escher o#er a classic illustration of this pictorialfreedom, whereby three-dimensionality is reduced to pattern making as a mode ofarchitectonic representation.

63 As Jay attempted to show, a ‘‘denigration of vision’’ has accompanied theradically critical stances taken with regard to space and the privileging oftemporal and chronological analyses over spatial ones. He furthermore takes this

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Consequently, the anticipation of modernity takes shape in theformation of Renaissance perspective, which is grasped againstthe background of mediaeval optics and mathematics.64

Alhazen’s theories of light and vision reconciled mathemat-ics with physics (Kitab al-Manaz*ir, I.1 [1–8]),65 and pointed tothe complexity of their co-entanglement in visual percep-tion. The mathematical preoccupations of our polymath didnot undermine his experimental (i‘tibar; experimentatio)penchant,66 nor did his passion for observational testing com-promise the primacy he accorded to geometrical ideality. Thephilosophical imports of his theory of visual perception gainfurther significance in the manner they could partly inspireconceptual attempts to surpass the epistemological and onto-logical limitations of intellectualism or empiricism, idealism or

state of a#airs to be the result of a modern French intellectual endeavour (fromthe times of H. Bergson to those of J. Derrida) to defy the epistemologicalbearings of the Enlightenment and its stress on rationality. Vision, the ‘‘noblestof the senses’’, is challenged in its capacity to o#er a reliable access to reality,and space is seen as being not only inert but is also grasped as an accommo-dating phenomenon that facilitates the exercising of oppressive power andviolence. See: Martin Jay, Downcast Eyes: The Denigration of Vision in Twentieth-Century French Thought (Berkeley, 1993); John Rajchman, ‘Foucault’s art ofseeing’, October, 44 (1988): 89–117, pp. 90, 95.

64 Architectural spaces are essentially formed by human situations that arecorporeally structured prior to being determined geometrically. Moreover, most ofour dealings with objects are conducted from an exteriority; for, in order to beable to experience the interiority of things we must go beyond their surfaces, toreveal the depth they enclose as well as open them up. Architectural spacesinvert this relation with objective surfaces in letting us dwell within an interioritythat is not the mere residual hollowness surrounded by an exterior con-taining enveloper, rather as a place that is corporeally inhabited. The dilemma ofmodernity, in aspiring to reconcile techno-scientific achievements with thesituational emplacement of the human condition in the natural world, is claimedto potentially find its inspiration in the latent capacity of architecture to gathermulti-layered levels of reality, and to relate abstract conceptual structures to theconcreteness of everydayness. This state of a#airs is seen as being of focalsignificance to the restoration of the topological and corporeal grounds of culturethat may shelter a sense of humanism in the age of modern technology. Regardingthe thrust of this line in interpretation, I refer the reader to: Dalibor Vesely,Architecture in the Age of Divided Representation (Cambridge, Mass., 2004).

65 Abdelhamid I. Sabra, ‘The physical and the mathematical in Ibnal-Haytham’s theory of light and vision’, in Commemoration Volume of BırunıInternational Congress in Tehran (Tehran, 1976), pp. 1–20; A. I. Sabra. Optics,Astronomy and Logic (Aldershot, 1994), chapter VII.

66 Abdelhamid I. Sabra, ‘The astronomical origin of Ibn al-Haytham’s conceptof experiment’, Actes du XIIe Congrès International d’Histoire des Sciences, Tome IIIA (Paris, 1971), pp. 133–6; Sabra, Optics, Astronomy and Logic, chapter IV; SalehBeshara Omar, Ibn al-Haytham’s Optics: A Study of the Origins of ExperimentalScience (Minneapolis, 1977).


realism, in an e#ort to re-think the elucidation of phenomenaand the nature of the relation between the imagined and theperceived, the mathematical and the physical. Such interroga-tions (or riddles) solicit corollaries that the history of scienceand philosophy might still assist us in re-thinking them anew,given that the classical is not simply past, nor merely handedover as present, but also comes to meet us in a future.

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a philosophical perspective on alhazen's optics

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